7804b5…: “Next to a tall calculation”

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1 : Consider the following set of ordered pairs that represent input-output values of a relation (ie for an ordered pair $(3, 7)$ the ‘input’ is $3$ and the ‘output’ is $7$ );

$(\sage {p1c1x}, \sage {p1c1y}), (\sage {p1c2x}, \sage {p1c2y}), (\sage {p1c3x}, \sage {p1c3y}), (\sage {p1c4x}, \sage {p1c4y}), (\sage {p1c5x}, \sage {p1c5y}), (\sage {p1c6x}, \sage {p1c6y}), (\sage {p1c7x}, \sage {p1c7y}), (\sage {p1c8x}, \sage {p1c8y}),$

Is this relation a function? Enter the number 1 if the above represents a function, or 0 if it does not. $\answer {\sage {p1ans}}$

Remember that, in order for something to be a function, it needs to have exactly 1 output for any given input. This means that if the same input appears more than once with a different associated output [that is, if you have two ordered pairs with the same $x$ value but different $y$ values] then the underlying relation cannot be a function.

2 : Consider the following set of ordered pairs that represent input-output values of a relation (ie for an ordered pair $(3, 7)$ the ‘input’ is $3$ and the ‘output’ is $7$ );

$(\sage {p2c1x}, \sage {p2c1y}), (\sage {p2c2x}, \sage {p2c2y}), (\sage {p2c3x}, \sage {p2c3y}), (\sage {p2c4x}, \sage {p2c4y}), (\sage {p2c5x}, \sage {p2c5y}), (\sage {p2c6x}, \sage {p2c6y}), (\sage {p2c7x}, \sage {p2c7y}), (\sage {p2c8x}, \sage {p2c8y}),$

Is this relation a function? Enter the number 1 if the above represents a function, or 0 if it does not. $\answer {\sage {p2ans}}$

3 : Consider the following set of ordered pairs that represent input-output values of a relation (ie for an ordered pair $(3, 7)$ the ‘input’ is $3$ and the ‘output’ is $7$ );

$(\sage {p3c1x}, \sage {p3c1y}), (\sage {p3c2x}, \sage {p3c2y}), (\sage {p3c3x}, \sage {p3c3y}), (\sage {p3c4x}, \sage {p3c4y}), (\sage {p3c5x}, \sage {p3c5y}), (\sage {p3c6x}, \sage {p3c6y}), (\sage {p3c7x}, \sage {p3c7y}), (\sage {p3c8x}, \sage {p3c8y}),$

Is this relation a function? Enter the number 1 if the above represents a function, or 0 if it does not. $\answer {\sage {p3ans}}$